Toward a Hajnal-Szemerédi theorem for hypergraphs
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چکیده
Let H be a triple system with maximum degree d > 1 and let r > 107 √ d log d. Then H has a proper vertex coloring with r colors such that any two color classes differ in size by at most one. The bound on r is sharp in order of magnitude apart from the logarithmic factors. Moreover, such an r-coloring can be found via a randomized algorithm whose expected running time is polynomial in the number of vertices of H. This is the first result in the direction of generalizing the Hajnal-Szemerédi theorem to hypergraphs.
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تاریخ انتشار 2010